The formula used to measure ocean depth using sound waves is called the echo sounding equation or the sonar equation. It relates the time it takes for a sound wave to travel from a source to the seafloor and back to the receiver to the depth of the ocean.
The basic form of the sonar equation is as follows:
D = (c × t) / 2
Where: D is the depth of the ocean. c is the speed of sound in water. t is the round-trip travel time of the sound wave.
In this equation, the round-trip travel time of the sound wave is divided by 2 because the time measured is the total time taken for the sound wave to travel from the source to the seafloor and back to the receiver.
To use this equation, the speed of sound in water must be known, as it can vary depending on factors such as water temperature, salinity, and pressure. On average, the speed of sound in seawater is approximately 1,500 meters per second (m/s).
By measuring the time it takes for the sound wave to travel to the seafloor and back, and knowing the speed of sound in water, the depth of the ocean can be calculated using the sonar equation. This method is commonly used in oceanography and hydrography for mapping the ocean floor and determining the bathymetry (depth profile) of the seafloor.